4 papers · 1 filter
The anisotropic part of a quadratic form over a number field
Przemysław Koprowski, Beata Rothkegel
It is well known that every non-degenerate quadratic form admits a decomposition into an orthogonal sum of its anisotropic part and a hyperbolic form. This decomposition is unique…
Computing singular elements modulo squares
Przemysław Koprowski
The group of singular elements was first introduced by Helmut Hasse and later it has been studied by numerous authors including such well known mathematicians as: Cassels, Furtwäng…
Graph of even points on an arithmetic curve
Alfred Czogała, Przemysław Koprowski
We show that the points of a global function field, whose classes are 2-divisible in the Picard group, form a connected graph, with the incidence relation generalizing the well kno…
Wild sets in global function fields
Alfred Czogała, Przemysław Koprowski, Beata Rothkegel
Given a self-equivalence of a global function field, its wild set is the set of points where the self-equivalence fails to preserve parity of valuation. In this paper we describe s…